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arXiv · 2607.05942

Exact flat bands in a 3D photonic crystal

Kin Hung Fung·Yan-Long Chen·C. T. Chan·Qinghua Guo
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Abstract

Photonic flat bands are hard to engineer because Maxwell's equations are vectorial: transversality obstructs the localized scalar-like bases that generate destructive-interference flat bands in tight-binding models. We show that a three-dimensional metallic network of dipolar cavities joined by waveguide channels--a fully vectorial photonic crystal belonging to space group No. 224--hosts an exact scalar sector, carrying exact flat bands. The twelve-band vector problem contains one self-adaptive radial dipole axis per site whose projection is exactly the scalar four-band Hamiltonian of the same network. A microwave-scale coupled-dipole calculation confirms this scalar-vectorial duality. The result is a symmetry-based design rule for scalar-like flat bands in reciprocal vector media.

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Kin Hung Fung, Yan-Long Chen, C. T. Chan, Qinghua Guo. 2026-07-07. Exact flat bands in a 3D photonic crystal. https://arxiv.org/abs/2607.05942

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